Answered: he table below contains data about the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The table below contains data about the yearly unemployment rate and poverty rate for Free State Province for a period of 10 years (from 2010 - 2019). Assume that unemployment rate and poverty rate are normally distributed. NB: use the values as they appear in the data table to obtain all of your estimates.

years	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019
Unemployment rate	3.5	4.4	5.2	2.8	3.9	4.0	3.8	3.3	4.8	3.1
Poverty rate	5.1	6.3	7.5	5.3	7.5	6.8	5.3	6.0	6.4	4.2

a. Use ordinary least squares (OLS) to fit the sample regression function (poverty rate)i=b0+b1(unemployment rate)i+ei to the data. Write down the estimated sample regression function and interpret your estimate of b1.

b. Estimate and interpret the coefficient of determination, R^2.

c. Does the poverty rate increase as unemployment increases? In other words, is the coefficient of unemployment rate (b1) positive? Test at the 5% level.

d. Estimate a 90% prediction interval for poverty rate, if unemployment rate =4.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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